Development of relationship between macroeconomic

Development of relationship between macroeconomic variables and stock market prices in the Czech Republic, Poland, Germany, Euro area, and the United Kingdom1 Lumír Kulhánek, Stanislav Matuszek

Abstract This paper is concerned with causal linkage among real economic variables, money supply and stock market development in the Czech Republic, Poland, Germany, Euro area, and the United Kingdom. The main objective is to investigate and evaluate long-run equilibrium relationships between macroeconomic variables and stock prices as well as short-run dynamics using Vector Error Correction Model in analysed countries. The empirical part exploits contemporary econometric tools such as unit root tests, Granger causality tests, Johansen Cointegration analysis. In analysis are used quarterly data in the sample period from 1995:Q1 to 2007:Q3. Money supply, national stock market indices and real gross domestic product are used in this study. The results of the analysis for two new EUEconomies will be compared with empirical observations from developed EU-Countries. Evidence suggests that the responses differ among these countries.

Key words: real GDP, stock market indices, money growth, long-run relationship, cointegration, errorcorrection model

1. Introduction The relationship between macroeconomic variables and asset prices, in general, has recently renewed interest among academics, researchers and policy-makers. One of interesting discussion is whether real output responds to developments in money supply and financial markets. Under the standard prevailing approach, changes in money supply affect real economic activities through various channels. These include the liquidity channel, stock price channel, wealth effects, and household liquidity effects. Basis on these explanatory models, we can discern that interactions among real economic activities, money, and stock market prices are bound in a dynamic way. Macroeconomic variables influence and are influenced by stock prices and monetary variables. In addition, economic variables interact with each other. Unfortunately, the direction of the interactions and which variable is leader (dominant, contemporaneous, or lagged) in the interactions remains unclear. Thus, the nature, 1

This paper is prepared with the support of the Grant Agency of the Czech Republic Project No. 402/08/0067 „Financial Integration of the EU Member States with Eurozone".

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direction, strength or weakness of the interactions among them in short-run and long-run is of high interest and needs to be investigated and evaluated empirically. Several studies modelled relationships between real economic activity and stock prices for the USA, the United Kingdom, and selected Central European countries.2 Following these authors we hypothesize a positive relation between gross domestic product and stock prices. Traditionally causality between money and stock prices has been assumed to run from money to stock prices. It is usually argued that a rise in the money demand facilitates an increase in output, profits and stock prices. As noted Friedman (1988) and number of other studies causality between money and stock prices have assumed to run from stock prices to money. A rise in stock prices could imply a rise in financial transactions both in the transaction money demand. A rise in stock prices caused through wealth effect higher wealth to income ratio and therefore higher money to income ratio. A rise in stock prices reflects a rise in expected return from risky assets relative to safe assets. To offset the subsequent rise in risk of an investor’s portfolio, relatively safe assets would be substituted for long-term bonds. All three factors should have produced a positive relationship between stock prices and money. To date there has been little attempt to determine in which direction causality actually runs in countries other than the USA.

2. Methodology of empirical analysis Attempts to measure and model economic or financial variables and analyses the relationships among such variables have involved virtually each principal econometric methodology. These problems that have arisen and were resolved have been extremely important in development of econometrics. The most important task of the econometrics is to quantify these relationships on the basis of available data and using statistical techniques, and to interpret, use or exploit the resulting outcomes appropriately. Consequently, econometrics is the interaction of economic theory, observed data and statistical methods. It is the interaction of these three that makes econometrics interesting, challenging and sometimes, perhaps, a little difficult. The number of econometric techniques that can be used in practice is numerous and their validity often depends crucially upon the validity of the underlying assumptions. An important goal of econometrics is to formulate such hypotheses in terms of parameters in the model and test their validity. 2

For the USA see Fama (1981), Huang and Kracaw (1984), Chen, Roll and Ross (1986), among others. For the United Kingdom see Poon and Taylor (1991), Cheng (1995), Kulhánek and Matuszek (2007), Hanousek and Filler (2000), among others.

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The traditional way of constructing of models, the large models with many variables, was not very dynamic (e.g. this approach involved only seldom lagged values of variables). 3 The main alternative approach, time series analysis, concentrated on dynamics and characteristics of time series. This approach paid little or no attention to economic or financial theories, and built models involving only a few variables.4 We try to reconcile both approaches. Our key assumption is that, while economic theory can explain the long-run trend of the markets, short-run movements are driven by variables that are not exactly specified and do not enter into the theory and thus have to be fitted empirically. We can identify our modelling approach as a short-run adjustment around long-run equilibrium. Developments in modelling tools (VAR models, cointegration analysis and Error-Correction models) provide us with methods that are powerful and relevant for the analysis of relationship between macroeconomic variables (real output and money supply) and stock market prices. According to Granger, economic or financial theory is adequate to describe a long-run equilibrium, but in the short-run the shocks or specific factors may push variables away from their equilibrium values. It then takes some time to move back to the long-run state. The key idea is that there is “reversion force” that it ensures the return to equilibrium. It is a very interesting theoretical and empirical question whether selected economic and financial variables are significant explanatory factors of real output. If these variables are significantly and consistently reflected, they should be cointegrated. Thus, cointegrating relation among real GDP, money supply, and stock markets indices is a necessary condition of the equilibrium models. Consequently, the presence of a cointegrating vector can be interpreted as the presence of a long-run equilibrium relationship. The main aim of our research is an investigation if real outputs are cointegrated with monetary aggregates and stock prices in analysed countries. Our empirical analysis includes five parts: - Unit-root tests, - Granger causality tests, - Vector autoregression (VAR models, Impulse-Response analysis, Variance Decomposition), - Johansen cointegration tests to find out that a set of variables are cointegrated or not, - Vector Error Correction models for cointegrated variables. 3

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The large simultaneous models were limited by some well-formulated, very often generally accepted economic or financial theories. Very often the models were (or they are) almost fully specified in basic theory and the only task remaining had been estimation of the parameters. Over the years these two dominant approaches have influenced and interacted with each other. Thus the large models became more dynamic and involved unit roots (stationary or non-stationary series) and cointegration. And the time series models considered number of variables (not only univariate models) and paid more attention to the use of theories.

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We use unit root tests to determine non-stationarity (or stationarity) of variables in original level and indicate which difference of time series is stationary. The Augmented DickeyFuller test and the Phillips-Perron test are used. Granger causality or non causality is concerned with whether lagged value of one variable (e.g. ”X”) do or not do improve on explanation of another variable (“Y”) obtainable from only lagged values of “Y” (Granger, 1969).5 We must note that the statement “X” Granger cause “Y” does not imply that “Y” is the effect or the result of “X”. Granger causality measures precedence and information content but does not indicate causality in the more common use of the term. Granger causality test is based on following two equations: K

K

i 1

j 1

Yt   y 0    i Yt i    j X t  j   t K

K

i 1

j 1

(Eq. 1),

X t   x 0    i X t i    j Yt  j  u t

(Eq. 2).

The reported F-statistics are the Wald statistics for the joint hypothesis:6

 j  0 ( 1   2   3  ....   K  0)

(Eq. 3).

In common tests, the null hypothesis is that “X” does not Granger-cause “Y” (in the first regression) and that “Y” does not Granger-cause “X” (in the second regression). A lag length (from ”i, j” to “K”) corresponds to relevancy, to reasonable beliefs about the longest time over which one of the variables could help predict the other.7 Vector autoregression (VAR models) is an econometric model used to capture the evolution and the interdependencies between multiple time series, generalizing the univariate AR models. All the variables in a VAR are treated symmetrically by including for each variable an equation explaining its evolution based on its own lags and the lags of all the other variables in the model.8 The VAR approach treats every endogenous variable as a function of the lagged values of all of the endogenous variables in the system. The principal mathematic representation of a VAR is:

Yt  A1Yt 1  A2Yt  2  ....  ApYt  p  BX t   t 5

(Eq. 4),

“Y” is said to be Granger caused by “X” if “X” helps to in prediction of “Y”, or equivalently if the coefficients on lagged “X” are statistically significant. In practice, two-way causation is frequently the case: “X” Granger cause “Y” and “Y” Granger cause “X”. 6 Note: γj for each equation. 7 In general, it is better to use more rather than fewer lags. (our opinion) 8 Based on this feature, Sims (1980) advocates the use of VAR models as a theory-free method to estimate economic relationships, thus being an alternative to the "incredible identification restrictions" in structural models.

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where Yt is a k-vector of endogenous variables, Xt is a l-vector of exogenous variables, A1, ... , Ap, and B are matrices of the coefficients to be estimated, e t is a vector of innovations.9 Impulse–Response analysis traces out the responsiveness of the dependent variables in the VAR model to shocks for each of the variables. So, for each variable from each equation separately, a unit shock is applied to the error, and the effects upon the VAR system over time are noted. This is, in practice, expressing the VAR model as a VMA (vector moving average) model. Provided that the system is stable, the shocks should gradually die away. Variance decomposition offers a slightly different method for examining VAR system dynamics. They give the proportion of the movements in the dependent variables that are due to their own shocks, versus shocks to the other variables. A shock to the i-th variable will directly affect that variable, but it will also be transmitted to all of the other variables in the system through the dynamic structure of the VAR. Thus, variance decomposition determines how much of sstep-ahead forecast error variance of a given variable is explained by innovations to each explanatory variable for s = 1, 2, … . In practice, it is usually observed that own series shocks explain most of the (forecast) error variance of the series in the VAR. Impulse-Responses and variance decomposition offers very similar information. More than twenty years have passed since the introduction of cointegration into econometric literature.10 It has become customery to investigate the existence of cointegrating relations among integrated (often called non-stationary) economic or financial variables before conducting formal inference, like estimating parameters of model or testing hypotheses. If the data are cointegrated, vector error correction model (VECM) can be estimated. Otherwise, vector autoregressive (VAR) model are estimated in first differences. Even though many economic series are routinely found to be cointegrated, it should be emphasized that cointegration is a very special phenomenon indeed. Cointegration occurs because economic data share common stochastic trends, which are eliminated by cointegrating linear combinations. Common stochastic trends are usually expressed as a linear combination of the shocks of a system. Putting it differently, economic data are cointegrated because they respond to shocks together. Cointegration of variables is at least a necessary condition for them to have a stable long-run relationship. However, if the no-cointegration hypothesis cannot be rejected, then

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The lag length specification (“p”) can be determined by information criteria (e.g. the AIC – Akaike Information Criterion or the SC – Schwarz Information Criterion). 10 See Granger (1981) and (1983); Engle and Granger (1987), among others.

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the estimated regression is just a “spurious” one and has no economic meaning. The Johansen (1988) maximum likelihood estimator circumvents these problems and enables to test for the presence of multiple cointegrating vectors. Johansen shows how to test for linear restrictions on the parameters of the cointegrating vectors. It makes possible to test the symmetry and proportionality conditions exactly. The details of the Johansen procedure are very complex and we shall only focus on a few aspects. The starting point of the Johansen procedure is the VAR representation of k-dimensional vector Yt of order p (lags):

Yt  A1Yt 1  A2Yt  2  ....  ApYt  p  BX t   t

(Eq. 5).

Assuming that Yt is a vector of non-stationary I(1) endogenous variables, Xt is a vector of deterministic exogenous variables (it can be a constant, linear terms or seasonal dummies), A1, …., Ap and B are k x k matrices of parameters, and εt is a vector of innovations or (in statistical sense) εt are k-dimensional independent Gaussian variables with mean zero and variance matrix Ω (εt ~ IID (0, Ω)). This can be written as: p 1

Yt  Yt 1   i Yt  i  BX t   t

(Eq. 6),

i 1

p

where

   Ai  I ,

and

i 1

p

i    A j . j  i 1

The Granger representation theorem (Engle and Granger, 1987) asserts that if the coefficient matrix Π has reduced rank r < k, then there exist k x r matrices γ and β with rank r such that Π = γβ' and β'Yt is I(0). The cointegration rank r is the number of cointegrating vectors. The elements γ are known as the adjustment parameters in VEC model. The Johansen method is to estimate the Π matrix from an unrestricted VAR model and to test whether we can reject (or not) the restrictions implied by the reduced rank of Π.11 Time series may have non-zero means and deterministic trends as well as stochastic trends. Similarly, the cointegrating equation may have intercepts and deterministic trends. The asymptotic distribution of the likelihood ratio test statistic for cointegration does not have the usual χ 2 distribution and depends on the assumptions made with respect to deterministic trends. Therefore, in order to carry out the test, we need to make an assumption regarding the trend underlying our data. However, the tests for cointegration assume that the cointegrating vector is constant during the period of study. In reality, it is possible that the long-run relationship between the 11

The main steps in the Johansen procedure and test hypotheses (the Trace statistic and the Maximum Eigenvalue statistic) are explained in Kulhánek and Matuszek (2004) in details.

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underlying variables change (shifts in the cointegrating vector can occur). The reason for this might be technological progress, economic crises, changes in the people’s preferences and behaviour accordingly, policy or regime alteration, and organizational or institutional developments. This is especially likely to be the case if the sample period is long.

3. Data The empirical analysis is based on quarterly data from 1995:Q1 to 2007:Q3. Stock prices are Prague Stock Exchange 50 Index (PX) for Czech Republic, Deutscher Aktienindex (DAX30) for Germany, Dow Jones Euro Stoxx 50 Index for Euro area, Warszawski Indeks Giełdowy (WIG) for Poland, and the Financial Times Stock Exchange Index 100 (FTSE100) for the United Kingdom. The GDP at 1995 constant prices is used as measure of real economic activity. Data are seasonally adjusted. Monetary aggregates M2 are used to represent money supply. For Germany, the United Kingdom and Euro area we examine money supply M2 based on harmonised definitions of the European Central Bank, for the Czech Republic and Poland monetary aggregates based on definitions of national central banks. Data are obtained from Eurostat, the European Central Bank and national central banks. All time series are transformed into natural logarithms prior to the empirical analysis. Fig. 1 shows development of stock market indices in the sample period from 1995 to 2007. Figure 2 and 3 shows the development of analyzed variables in the Czech Republic, Germany, Poland and Euro area. Fig. 1 Stock markets indices (1995:Q1 – 2007:Q3)

800

600

400

200

0 95 96 PX

97

98 99 DAX

00

01 02 DJE50

03

04 05 WIG

06

07 FTSE

Source: Own calculations based on http://epp.eurostat.ec.europa.eu.

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Fig. 2 Product, money supply, and stock prices in Czech Republic and Germany Czech Republic

350

Germany

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300

300

250

250

200

200

150

150

100

100

95 96 97 98 99 00 01 02 03 04 05 06 07 GDP M2 PX

95 96 97 98 99 00 01 02 03 04 05 06 07 GDP M2 DAX

Source: Own calculations based on http://epp.eurostat.ec.europa.eu, http://www.cnb.cz, www.bundesbank.de.

Fig. 3 Product, money supply, and stock prices in Poland and Euro area Poland

Euroarea

800

800

600

600

400

400

200

200

95

96

97

98

99 00 GDP

01

02 M2

03

04 05 WIG

06

07

95

96

97

98

99 00 GDP

01

02 M2

03

04 05 DJE50

06

07

Source: Own calculations based on http://epp.eurostat.ec.europa.eu, http://www.nbp.pl.

4. Results of tests and evaluation of models Tests of stationarity are a matter of concern in very important areas. In our study it is one of the crucial tests for entering to cointegration analysis and analysis of equilibrium space. We used common conventional unit-root tests as the Augmented Dickey -Fuller (ADF)

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and the Phillips–Perron (PP) tests.12 The results of unit-roots testing in Table 1 show that the null hypothesis of non-stationarity is not rejected for all variables in original levels and in natural logarithm of levels of variables, but is rejected for variables in first differences. 13 Therefore, each variable is integrated of order 1, or I(1), and it is possible to test if the levels of these variables are cointegrated. Table 1: Unit root tests for stock prices, money supply and real GDP Levels of variables (in logs) First differences of variables (in logs) Model C Model CT Model C Model CT ADF PP ADF PP ADF PP ADF PP M -1.59 -1.77 -2.84 -5.30*** -8.48*** -8.45*** -8.59*** -8.55*** Czech Rep. SP 0.24 0.59 -0.96 -1.18 -5.62*** -5.67*** -5.73*** -5.75*** GDP 3.37 2.25 0.77 -0.15 -9.46*** -9.02*** -10.90*** -9.93*** M -0.63 -0.93 -2.36 -2.77 -3.18** -9.77*** -3.04 -9.92*** Germany SP -1.97 -1.62 -2.03 -1.68 -4.43*** -4.47*** -4.41*** -4.44*** GDP -0.30 -0.14 -2.03 -1.99 -9.47*** -9.35*** -9.37*** -9.26*** M 2.50 4.82 0.20 -1.86 -1.13 -14.68*** -2.69 -33.36*** Euro area SP -2.07 -1.99 -1.84 -1.76 -4.80*** -4.82*** -4.87*** -4.89*** GDP -0.30 -0.28 -1.73 -1.68 -7.85*** -7.85*** -7.77*** -7.77*** M -2.32 -4.38*** -2.59 -2.91 -2.44 -5.10*** -2.77 -6.50*** Poland SP -0.20 -0.35 -1.06 -1.33 -6.20*** -6.20*** -6.21*** -6.21*** GDP -1.04 -1.12 -2.87 -2.88 -8.47*** -8.55*** -8.43*** -8.50*** 1.86 1.93 0.01 0.22 -6.69*** -6.70*** -7.08*** -7.09*** U. Kingdom M SP -1.92 -2.13 -1.80 -1.96 -4.85*** -4.81*** -4.86*** -4.82*** GDP -1.10 -0.98 -2.07 -3.25* -11.73*** -13.46*** -11.76*** -15.43*** Model C is the model with non-zero mean. Model CT is the model with non-zero mean and linear trend. Lag length for each AR process of ADF test is automatic based on SIC. (*), (**) and (***) indicate the rejection of the corresponding null hypothesis at the 10*, 5%, 1% significance levels. Source: authors´ calculations by EViews 5.1.

Table 2 shows results of Granger causality. The results can be taken into consideration in several of reasons. For example, the question of interest may be exogenity variables in a bivariate regression model (Eq.1 and Eq. 2).14 We must note that we should be careful when comparing the test results because number of available observations is low (1), and Granger causality tests are based on the first differenced (de-trended) variables (2). Thus, very important trend information is eliminated. Despite of these facts, the results show a rich, but non-stable structure of Granger causality relationships in examined countries.

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Tests exploit automatic selections of lag length and bandwidth. We used also the newest generation of unit-root tests as the Ng–Perron (NP), the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests, and the Elliot– Rothemberg–Stock (ERS–Point optimal, GLS–Detrended DF) tests. We employed these tests to ensure robustness of our inferences. 13 First difference: dXt = Xt – Xt-1. 14 Three main purposes are distinguished: 1. to make inferences about parameters of regression, 2. to forecast “Y” (or “X”) conditional on “X” (“Y”) (see Eq.1 and Eq.2), and 3. to test whether the relation in Eq.1 (or Eq.2) is structurally invariant to changes in the marginal distribution of “X” (or “Y” alternatively). Corresponding to these three purposes are three types of exogenity, namely, weak, strong, and super exogenity. Engle, Hendry, Richard (1983).

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Table 2: Granger causality tests – probability (p-value) of the Null Hypothesis Czech Republic SM does not GC GDP GDP does not GC SM M does not GC GDP GDP does not GC M M does not GC SM SM does not GC M Poland SM does not GC GDP GDP does not GC SM M does not GC GDP GDP does not GC M M does not GC SM SM does not GC M Germany SM does not GC GDP GDP does not GC SM M does not GC GDP GDP does not GC M M does not GC SM SM does not GC M Euro area SM does not GC GDP GDP does not GC SM M does not GC GDP GDP does not GC M M does not GC SM SM does not GC M United Kingdom SM does not GC GDP GDP does not GC SM M does not GC GDP GDP does not GC M M does not GC SM SM does not GC M

Lags 1 0,085 0,193 0,963 0,421 0,407 0,201

2 0,164 0,309 0,065 0,104 0,424 0,559

3 0,428 0,489 0,002 0,762 0,217 0,911

1 0,012 0,803 0,274 0,154 0,089 0,040

2 0,041 0,321 0,186 0,081 0,167 0,280

3 0,124 0,445 0,529 0,136 0,143 0,046

1 0,022 0,118 0,258 0,620 0,021 0,334

2 0,011 0,161 0,500 0,704 0,000 0,249

3 0,045 0,316 0,310 0,947 0,001 0,495

1 0,036 0,243 0,341 0,998 0,108 0,003

2 0,034 0,254 0,509 0,965 0,106 0,010

3 0,089 0,262 0,714 0,996 0,127 0,006

1 0,047 0,227 0,351 0,349 0,849 0,499

2 0,133 0,558 0,089 0,517 0,862 0,787

3 0,247 0,729 0,163 0,529 0,872 0,830

4 0,346 0,186 0,002 0,477 0,145 0,558

5 0,342 0,089 0,497 0,510 0,393 0,298 Lags 4 5 0,264 0,384 0,856 0,845 0,853 0,511 0,309 0,175 0,138 0,145 0,111 0,030 Lags 4 5 0,098 0,156 0,443 0,576 0,192 0,086 0,843 0,710 0,002 0,001 0,671 0,524 Lags 4 5 0,081 0,154 0,443 0,486 0,843 0,608 0,873 0,862 0,317 0,373 0,003 0,003 Lags 4 5 0,340 0,326 0,838 0,927 0,193 0,333 0,693 0,790 0,562 0,742 0,647 0,866

6 0,611 0,068 0,942 0,606 0,518 0,407

7 0,568 0,282 0,961 0,216 0,834 0,102

8 0,623 0,317 0,989 0,240 0,806 0,278

6 0,400 0,923 0,287 0,150 0,057 0,012

7 0,031 0,089 0,587 0,410 0,080 0,065

8 0,057 0,587 0,206 0,140 0,107 0,071

6 0,336 0,223 0,840 0,339 0,005 0,522

7 0,211 0,165 0,105 0,251 0,010 0,258

8 0,236 0,209 0,073 0,281 0,033 0,263

6 0,196 0,038 0,802 0,445 0,529 0,006

7 0,155 0,041 0,869 0,405 0,650 0,017

8 0,186 0,001 0,944 0,107 0,855 0,021

6 0,104 0,971 0,175 0,882 0,208 0,645

7 0,145 0,975 0,029 0,726 0,264 0,820

8 0,070 0,992 0,015 0,683 0,187 0,884

If probability is ≥ 0.05, then a null hypothesis is accepted; if probability is < 0.05, then a null hypothesis can be rejected. Note: GC–Granger cause, SM–Stock Market Index, GDP–Gross Domestic Product (in constant prices), M-Monetary supply M2. Source: authors´ calculations by EViews 5.1.

The main aim of our study is to investigate if money supply and stock market have an influence upon real economic output. In line with this aim, we can detect important relationships among growth of monetary aggregate M2 (gM2), stock market returns (rSM), and growth of real GDP in analysed countries (Table 3), but at a different significance levels.

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In Euro area we can state only interaction between stock market returns and growth of real GDP. In some cases, Germany and the UK, growth of monetary aggregate M2 and stock market returns can be seen as strong exogenous variables for parameters of models in which growth of real GDP is dependent variable. In the Czech Republic, we fined out that growth of monetary aggregate M2 is a strong exogenous variable for parameters of real GDP model. Table 3: Weak and Strong exogenity Country Czech Republic Poland Germany Euro area United Kingdom

Exogenity Weak gM2, rSM rSM gM2, rSM rSM gM2, rSM

Strong gM2 gM2, rSM gM2, rSM

Source: authors´ evaluations by EViews 5.1.

Table 4: Evaluations of the VAR models for dependent variable the real GDP growth Czech Rep. Poland Germany Euro area U. Kingdom R-squared 0.797369 0.546024 0.318435 0.226276 0.470658 Adjusted R-squared 0.723685 0.219161 0.070594 -0.055078 0.278170 S.E. of regression 0.350301 1.180478 0.777758 0.661687 0.566201 Mean dependent var. 0.781518 1.034414 0.393981 0,509120 0.702570 S.D. dependent var. 0.666405 1.335910 0.806755 0,644184 0.666428 Sum squared resid. 4.049447 34.83820 19.96194 14,44838 10.57926 Durbin-Watson stat. 1.208024 1.531568 2.056330 2.072402 2.134633 The lag length in the VAR models is 4 for the Czech Republic, Germany, Euro area, and the UK or 6 for Poland. The lag length specification is based on information criteria (the AIC, the SC). Source: authors´ calculations by EViews 5.1.

The VAR models are commonly used for analysing and forecasting system of interrelated time series or for analysing the dynamic impact of random disturbances on the system of variables. Summary statistic evaluation for the VAR (unrestricted) models is in Table 4. From the results of the VAR models we can note: -

the good model for the Czech Republic (but autocorrelations in the residuals, DW stat. is 1.2),

-

under the average model for Poland (autocorrelations in the residuals, DW stat. is 1.5) and the UK (autocorrelations in the residuals, DW stat. is 2.1),

-

the weak model for Germany, the VAR model for Euro area is a (completely) wrong. We must note that the VAR model is, as a matter of fact, the system of linear

regression equations. Thus, entering variables must be stationary (weak or covariance stationary). In practice commonly they are in the first differences. So, the VAR models reflect (mainly) the short-run dynamics of the variables, but they are not able to capture the long-run equilibrium relationships among the variables.

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To examine further dynamic interactions among variables, we generate impulseresponse functions from the estimated VAR models.15 We present the plots of the impulseresponse functions as interactions between the growth of real GDP and other variables in Figure 4 for the Czech Republic and Poland and in Appendix 1 for other countries. Fig. 4 Response of the GDP growth for the Czech Republic and Poland Response of DCZ_RGDPSA to Cholesky One S.D. Innovations

Response of DPL_RGDPSA to Cholesky One S.D. Innovations

.4

1.2

.3 0.8 .2 0.4

.1 .0

0.0

-.1 -0.4 -.2 -.3

-0.8 1

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DCZ_PX

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DPL_WIG

From Figures we may find out several notable points. It can be noted a short-run and a long-run positive lagged response of the real GDP growth to the stock market returns and a negative response to the monetary aggregate M2 growth shocks for the Czech Republic. In short-run horizon, it can be shown a positive impact of the growth of monetary aggregate M2 and the stock market returns on the growth of real GDP in Poland and Germany, and a negative response of the growth of real GDP to the growth of monetary aggregate M2 shocks in the United Kingdom (in very short-run). Interestingly, the growth of monetary aggregate M2 shocks and the stock market returns shocks have an alternating and a very weak impact on the growth of real GDP for Euro area and for the United Kingdom. Figures 5 and 6 show results for variance decompositions at time horizon of 10 quarters. The plots suggest the presence of interactions among the growth of real GDP, the growth of monetary supply M2, and stock market returns. Focusing on the table in Appendix 2, we may observe that variations in the growth of real GDP are predeterminantly attributed to its own variations in all countries and in Euro area. As we can see, very interesting situation is in the Czech Republic. Variation of monetary aggregate M2 growth is accounted for about 32 % 15

The VAR model (Eq. 4) may be written as the VMA (vector moving average) representation. The VMA is more easily interpreted as its moving average representation from which it may be generated impulseresponse functions and variance decomposition. This approach involves orthogonalizing innovations in each of the variables using Choleski decomposition of the residual covariance matrix, imposing a recursive structure on the contemporaneous relationship among variables.

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of the real GDP growth forecast error variance after 10 quarters. In addition, the innovations in the stock market returns also explain quite sizable fractions of the real GDP growth variation, namely, almost 16 % may be attributed to this variable. Fig. 5 Variance Decomposition of real GDP growth in the VAR models for the Czech Republic and Poland Variance Decomposition of DPL_RGDPSA

Variance Decomposition of DCZ_RGDPSA

100

100

80

80

60

60

40

40

20

20

0

0 1

2

3

4

5

DCZ_RGDPSA

6

7

8

DCZ_M2

9

1

10

2

3

4

5

DPL_RGDPSA

DCZ_PX

6

7

8

DPL_M2

9

10

DPL_WIG

Fig. 6 Variance Decomposition of real GDP growth in the VAR models for Germany, Euro area and the United Kingdom Variance Decomposition of DDE_RGDPSA

Variance Decomposition of DEA_RGDPSA

100

100

80

80

60

60

40

40

20

20

0

0

1

2

3

4

DDE_RGDPSA

5

6

7

8

DDE_M2

9

10

1

2

3

4

5

DEA_RGDPSA

DDE_DAX

Variance Decomposition of DUK_RGDPSA

80

60

40

20

0 2

3

4

5

DUK_RGDPSA

6

7

DUK_M2

13

8

9

7

DEA_M2

100

1

6

10

DUK_FTSE

8

9

10

DEA_DJE50

Looking at the other countries and Euro area, we can note the importance of the growth of monetary aggregate M2 to variation of the real GDP growth in Poland (10,75 %), in Germany (8,38 %), and in the United Kingdom (10,57 %) after 10 quarters. The stock market returns are the important factors of the real GDP growth variation in Poland (12,41 %), in Germany (4,18 %), in Euro area (13,33 %), and in the United Kingdom (6 %) after 10 quarters. The surprise is the very weak importance of the monetary aggregate M2 growth variation to variation of real GDP growth in Euro area (only 1,36 %). Next, we test the number of significant cointegrating vectors for each country.16 We used the Johansen approach to test for cointegration among real GDP (natural logarithm of real GDP), money supply (natural logarithm of monetary aggregate M2) and stock market indexes (natural logarithm of values). Table 5 displays the results of test. We can note that there are sufficient evidences for one non-zero cointegrating vector in unrestricted models. These tests indicate that a set of variables is cointegrated. Thus, for each set of variables we can form at most one cointegration equation. Model 2 and 3 are used in this paper for the VEC models. Table 5: Number of cointegrating equations and type test models Data Trend: None None Linear Linear Quadratic Test type: Model 1 Model 2 Model 3 Model 4 Model 5 Czech Republic Trace 2 2 1 2 3 Max-Eig 2 1 1 2 1 Poland Trace 1 2 1 1 3 Max-Eig 1 1 1 1 3 Germany Trace 1 1 1 2 3 Max-Eig 1 1 0 0 0 Euro area Trace 1 1 3 2 2 Max-Eig 1 1 1 2 2 United Kingdom Trace 1 1 0 0 0 Max-Eig 1 1 0 0 0 Number of Cointegrating Relations by Test Model. The Johansen approach to cointegration tests considers five test type cases: Model 1. the level data have no deterministic trends and the cointegrating equation do not have intercepts, Model 2. the level data have no deterministic trends and the cointegrating equation have intercept, Model 3. the level data have linear trends and the cointegrating equation have only intercepts, Model 4. the level data and the cointegrating equation have linear trends, Model 5. the level data have quadratic trends and the cointegrating equation have linear trends. Selected on 0.05 level of significance. Critical values based on MacKinnon-Haug-Michelis (1999). The lag order of the underlying test VAR is 4 (by the AIC procedure). Source: Own calculations.

The Granger representation theorem (Granger, 1983; Engle and Granger, 1987) states that if a set of variables are cointegrated, then there exists a valid Vector Error-Correction (or 16

Cointegration can be seen as the statistical notion corresponding to the theoretical concept of long-run equilibrium and implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are non-stationary and have infinite variance (Engle and Granger, 1987). Formally, if two or more non-stationary time series share a common trend, then they are said to be cointegrated.

14

equilibrium-correction) representation of the data. In this paper, the vector error-correction model is used to the real GDP growth. In this model, the real GDP growth is dependent variable. Money supply growths and stock market returns (∆smi) are explanatory variables. In error correction models, four additional lagged first differences of variables are used in regression equations for the Czech Republic, Germany, Euro area and the United Kingdom and six for Poland. Tables 6 and 7 show theoretical structure and estimated parameters of the VEC models. We can evaluate estimated parameters of models by t-statistics or probability. 17 Table 6: Error (Equilibrium) Correction Models for the growth of real GDP k

k

k

i 1

i 1

i 1

rgdpt  1   1  rgdpt 1   mt 1   smit1  c    1,i rgdpt i  1,i mt i   1,i smit 1  1,t

rgdp Czech Republic rgdp/ m2/ smi

1

Poland rgdp/ m2/ smi

1

Germany rgdp/ m2/ smi

1

Euro Area rgdp/ m2/ smi

1

UK es50def / m1

1

Cointegrating Vector β m2 smi c -0,411 (0,013) [-8,13] -0,150 (0,023) [-6,43] -0,357 (0,026) [-13,78] -0,350 (0,023) [-14,95] -0,260 (0,051) [-5,127]

-0,104 (0,026) [-15,62] -0,153 (0,018) [-8,56] -0,025 (0,012) [-2,04] -0,103 (0,013) [-7,62] -0,100 (0,061) [-1,626]

-2,104

-3,189

-2,814

-2,448

-2,961

Adj. Coeff.  -0,097 (0,013) [-7,55] -0,496 (0,198) [-2,51] -0,387 (0,132) [-2,928] -0,228 (0,056) [-4,030] -0,013 (0,033) [-0,384]

R2 R2 adj.

F-stat. Log. Lik.

AIC BIC(SC)

0,927 0,897

31,306 225,97

-9,216 -8,660

0,640 0,355

2,247 150,44

-5,929 -5,118

0,462 0,244

2,118 171,23

-6,836 -6,279

0,487 0,278

2,335 182,64

-7,332 -6,775

0,473 0,259

2,210 180,48

-7,238 -6,682

Notes: (...) – standard deviation, [...] – t-stat. Variables: ∆rgdp (lnrgdp - lnrgdp(-1)) = real GDP growth, α and c – intercepts, β – cointegration vector, γ – adjustment coefficient, φ and λ – coefficients (parameters) of cointegrating equations (cointegrating vector), δ,θ, and π – coefficients (parameters) of models (short-run coefficients), ε – errors. Source: authors´ calculation by EViews 5.1.

Table 7: VEC models - dependent variable is the growth of real GDP (∆rgdp) Country : variables

Adjust. Coeff.

 value (probability)

Standard errors

t-statistics

Czech Republic: rgdp/ m2/ px

-0.097178 (0.0000)

0.012877

-7.546676

Poland: rgdp/ m2/ wig

-0.495915 (0.0145)

0.197873

-2.506228

Germany: rgdp/ m2/ dax

-0.387280 (0.0043)

0.132245

-2.928501

Euro area: rgdp/ m2/ djes50

-0.227748 (0.0001)

0.056511

-4.030148

UK: rgdp/ m2/ ftse

-0.012544 (0.7012)

0.032595

-0.384859

Source: authors´ calculation by EViews 5.1.

17

It is possible to verify statistic significance of cointegrating vectors in error correction models using the Wald tests as well.

15

Looking at the Table 6 and Table 7 we can conclude that long-run equilibrium relationship is enforced in the all countries except the United Kingdom. In the United Kingdom the cointegration relationship is statistically insignificant. Probably, the reason is another short-run dynamic fluctuations of money supply and/or stock prices. Outputs of the VEC models for analyzed countries are presented in Figures 7 and 8. Fig. 7 VEC models for GDP growth in the Czech Republic and Poland Czech Republic (Model 3, lags 4) Poland (Model 3, lags 6) .06

.02

.04

.01

.02 .00

.00

.004 .002

-.01

.02

-.02

.01

-.04

.000

.00

-.002

-.01 -.02

-.004 96

97

98

99

00

01

Residual

02

03

04

Actual

05

06

97

07

98

99

00

01

02

Residual

Fitted

03

04

Actual

05

06

07

Fitted

Fig. 8 VEC models for GDP growth in Germany, Euro area and the U.K. Germany (Model 2, lags 4) Euro area (Model 2, lags 4) .04

.04

.03

.03

.02

.02

.01

.01

.00

.02

.02

.00

-.01 .01

.01

-.02

.00

.00

-.01

-.01

-.02

-.01

-.02 96

97

98

99

00

Residual

01

02

03

04

Actual

05

06

07

96

97

98

Fitted

99

00

01

Residual

02

Actual

United Kingdom (Model 2, lags 4) .03 .02 .01 .010

.00

.005

-.01

.000 -.005 -.010 -.015 96

97

98

99

00

Residual

16

01

02

03

Actual

04

05

06

Fitted

03

07

04

05

06

Fitted

07

In the end of our study, we compare possibilities and usefulness of both VEC and VAR models for GDP growth modelling. As we can see in Table 8, if long-run cointegration relationship is present, then the VEC models are much more usefull then the VAR model. For the United Kingdom both models are comparable. Table 8: Comparison of the VEC vs. theVAR models for the growth of real GDP Country : variables

VEC

VAR

R2-adj.

DW-stat.

R2-adj.

DW-stat

Czech Republic: rgdp/ m2/ px

0.897

1.949

0.724

1.208

Poland: rgdp/ m2/ wig

0.355

1.529

0.219

1.531

Germany: rgdp/ m2/ dax

0.244

1.987

0.071

2.056

Euro Area(EMU): rgdp/ m2/ djes50

0.278

2.186

-0.055

2.072

UK: rgdp/ m2/ ftse

0.259

2.135

0.278

2.135

Source: authors´ calculation by EViews 5.1.

Conclusions In this study we have addressed the relationship and interaction among the measure of real economic activity (represented by the real GDP), money supply (monetary aggregate M2), and stock market development (stock market indices) in the Czech Republic, Poland, Germany, the United Kingdom, and Euro area. The empirical part of our study exploits appropriate econometric techniques to test stationarity (unit root tests), Granger causality (bivariate regression models), short-run dynamics (the VAR models, Impulse-Response analysis, Variance Decomposition), and long-run relationship (Johansen cointegration tests, the VEC models). The evidence obtained from analysis of time-series quarterly data from 1995:Q1 to 2007:Q3 suggest that in all cases we can find out the long-run equilibrium relationships (cointegration) among the real GDP, money supply (M2), and stock market indices. This is the most important result of our study. Thus, we may conclude that the monetary aggregate M2 and the stock market development have a certain predictive content for the real economic activity in the long-run horizon. We can also claim positive influences of money supply (M2) and the stock market development (stock market indices) on the real economic output for all countries and Euro area in the long-run. Looking at the results of the short-run analyses, we have to accept the great difference among countries, especially for the Czech Republic and the other analysed countries. This

17

conclusion is confirmed by Impulse-Response analysis both Variance Decomposition for example. Based on results of comparisons and evaluations of the VEC and the VAR models, we may state that the VEC models are the significantly better when the cointegrating relationships are enforced.

Appendix 1: Response of the GDP growth for Germany, Euro area, and the United Kingdom Germany

Euro area

Response of DDE_RGDPSA to Cholesky One S.D. Innovations

Response of DEA_RGDPSA to Cholesky One S.D. Innovations

.8

.7 .6

.6 .5 .4

.4 .3

.2 .2 .1

.0

.0 -.2 -.1 -.2

-.4 1

2

3

4

DDE_RGDPSA

5

6

7

8

DDE_M2

9

1

10

2

3

4

5

DEA_RGDPSA

DDE_DAX

United Kingdom .6 .4 .2 .0 -.2 -.4 -.6 2

3

4

5

DUK_RGDPSA

6

7

DUK_M2

18

8

9

7

DEA_M2

Response of DUK_RGDPSA to Cholesky One S.D. Innovations

1

6

10

DUK_FTSE

8

9

10

DEA_DJE50

Appendix 2: Variance Decomposition of real GDP growth for the VAR models Czech Rep.

Poland

Germany

Euro area

U. Kingdom

Period 1 2 3 4 5 6 7 8 9 10 Period 1 2 3 4 5 6 7 8 9 10 Period 1 2 3 4 5 6 7 8 9 10 Period 1 2 3 4 5 6 7 8 9 10 Period 1 2 3 4 5 6 7 8 9 10

S.E. 0.350301 0.432781 0.510339 0.577884 0.636711 0.669568 0.691700 0.713116 0.730219 0.737970 S.E. 1.180478 1.376436 1.478323 1.568811 1.577739 1.635277 1.660676 1.664467 1.669709 1.680534 S.E. 0.777758 0.855914 0.883453 0.903161 0.923107 0.926667 0.930489 0.933211 0.936827 0.937446 S.E. 0.661687 0.694176 0.714851 0.718625 0.741025 0.742292 0.745253 0.747177 0.747925 0.748176 S.E. 0.566201 0.729114 0.758417 0.761380 0.769439 0.776063 0.780292 0.781886 0.783641 0.784570

DCZ_RGDPSA 100.0000 93.24413 91.73088 80.54563 69.32065 63.80189 60.00128 56.45162 53.89090 52.83193 DPL_RGDPSA 100.0000 97.44767 85.23592 78.43651 78.35977 78.15714 77.35679 77.10869 77.07706 76.83233 DDE_RGDPSA 100.0000 98.82788 94.55828 91.03182 89.10145 89.06473 88.36736 88.12188 87.49263 87.43366 DEA_RGDPSA 100.0000 97.09065 92.38712 91.68835 86.27241 86.13379 85.93959 85.49805 85.35074 85.31524 DUK_RGDPSA 100.0000 95.15741 88.39368 88.10148 86.37372 85.03929 84.23169 83.92323 83.62883 83.43094

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DCZ_M2 0.000000 2.103361 3.637110 14.52983 25.04835 28.83782 30.31318 31.22918 31.73922 31.64009 DPL_M2 0.000000 1.083000 11.00087 10.01138 9.966592 10.35830 10.74570 10.77265 10.78452 10.75379 DDE_M2 0.000000 0.038275 1.448961 4.723812 6.807406 6.831264 7.561879 7.738640 8.356481 8.384628 DEA_M2 0.000000 0.320693 0.321698 1.010972 0.962764 0.959754 1.094115 1.181366 1.351560 1.357036 DUK_M2 0.000000 0.222776 7.286147 7.611904 9.248906 9.996838 10.45167 10.57157 10.59626 10.57219

DCZ_PX 0.000000 4.652507 4.632007 4.924541 5.631001 7.360285 9.685538 12.31920 14.36988 15.52798 DPL_WIG 0.000000 1.469326 3.763209 11.55211 11.67363 11.48455 11.89750 12.11866 12.13842 12.41388 DDE_DAX 0.000000 1.133845 3.992759 4.244370 4.091147 4.104009 4.070757 4.139482 4.150893 4.181709 DEA_DJE50 0.000000 2.588657 7.291185 7.300675 12.76483 12.90646 12.96630 13.32059 13.29770 13.32773 DUK_FTSE 0.000000 4.619819 4.320177 4.286618 4.377374 4.963869 5.316644 5.505208 5.774908 5.996871

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